Not quite sure what you are trying to do - only visible light makes sense to us from a color perception point of view.
Are you trying to make a cheap thermal camera? You probably already know that the images from those are in pseudocolor, that is, they return a monochrome image to which a colormap is applied to map intensities to color. Also, thermal cameras detect much longer wavelengths than a normal CCD or CMOS sensor can detect, so your cheap webcam sensor won't work.
If you are trying to highlight certain parts of your scene that reflect specific wavelengths of IR, you could try:
Bandpass IR filters are quite expensive, but if you can afford them, taking multiple photos with different bandpass IR filters in front of the sensor would work, and you would get the images at each IR band at the full resolution of your sensor. (Assuming your remove the IR / Bayer filters first.)
If you know the specific wavelengths you want to see, then try illuminating your scene with LEDs that emit light of known wavelengths. You would then have multiple images of your scene reflecting known wavelengths. Assuming there is no fluorescence or any other wavelength shifting phenomenon, then you'll be okay.
If you are just trying to colorize your IR photos, then converting to monochrome with a tint or a duotone in Photoshop/GIMP is your best bet.